1. Technical Field of the Invention
This invention lies in the field of seismic transducers and particularly velocity- and acceleration-sensitive instruments.
2. Discussion of the Prior Art
The geophysical industry, in the conduct of land seismic surveys for oil, has generally used geophones whose electrical outputs are representative of particle velocity.
Geophones as provided by suppliers of such instruments are characterized by a fixed natural or resonant frequency and are damped by a prescribed fraction of critical damping. If the geophysicist desired to resurvey a particular area using geophones having a different natural frequency, such as for the purpose of better noise cancellation or for high resolution studies, he was obliged to buy a complete new set of geophones. He had no means for altering the characteristics of his geophones. That is, the geophysicist had no convenient means for changing, in the field, the response characteristics of a given geophone.
There are of course, advantages to the use of velocity geophones such as their relatively low electrical impedance and relatively high output signal. But there are also certain disadvantages to use of a geophone such as the inflexibility of its characteristic parameters and the mechanical delicacy of the sensing element, a spring-suspended moving coil. In an actual exploration project, the geophysicist must not only carry an inventory of replacement geophones, but he may also be obliged to maintain two or three complete sets of geophones, each set having a different natural frequency with a different damping coefficient.
Recently, the use of accelerometers in place of geophones has received considerable interest. There are several advantages in the use of an accelerometer in place of a geophone: The accelerometer has a better response to higher seismic frequencies; for mechanical reasons, an accelerometer is believed to couple more efficiently to the ground; an accelerometer may be made less complex mechanically and electrically and is more rugged than is a geophone and accordingly can be considerably less expensive. An undamped accelerometer, used at frequencies below its natural frequency, has substantially no phase distortion. Finally, an accelerometer is a flexible instrument in that it can be used either as an accelerometer as such, or it can be easily tuned to match its output to the output response of any desired geophone, thereby serving as a multi-purpose seismic transducer.
If accelerometers are to replace geophones in seismic exploration, particularly in areas that were previously surveyed exclusively by use of geophones, the accelerometer output response characteristic, that is, its transfer function, must be capable of being modified to match the output or transfer function that is inherent to a selected geophone.
At first glance, it might be thought that the obvious approach entailing forming the time integral of the accelerometer output signal would yield the desired velocity signal as generated by a geophone since acceleration is the first time derivative of velocity. See for example Pavey, U.S. Pat. No. 3,281,768 or Sykes, U.S. Pat. Nos. 3,320,580 and 3,320,582. As will be seen below however, simple integration of the signal, as by an RC circuit, is not sufficient.
A seismic transducer, be it a geophone or an accelerometer, is a spring-mass system. Since the transducer is an oscillating system, it has a natural frequency. The natural frequency is defined to be that frequency at which the undamped system will oscillate when excited by a step function. At the natural or resonant frequency, an ideal frictionless system would theoretically oscillate forever at a fixed amplitude in response to a transient impulse. However, any real-world system includes some frictional or other energy-dissipative forces which tend to decrease or damp the amplitude of oscillation. Critical damping is the minimum damping required to prevent an excited system from oscillating. Generally, except for special applications, the damping force is some substantial fraction of critical.
Any spring-mass system, when operated above the natural frequency, measures displacement. When provided with a velocity-sensing device such as a coil of wire, mounted on the mass and arranged to cut a magnetic field, the system output signal is representative of particle velocity. The same spring-mass system, when operated well below its natural frequency, produces an output that is representative of particle acceleration.
In seismic exploration, geophones are of the well-known moving coil type; thus, their output signal is representative of particle velocity. Their natural frequency is usually in the range of 8-20 Hz and the damping coefficient is often set between 50% and 70% of critical damping. Above the natural frequency and for a velocity input of constant amplitude in the useful seismic frequency band, the geophone output response is substantially constant with increasing frequency. Below the natural frequency, lower frequencies are attenuated 12 dB per octave. Of the 12 dB attenuation, 6 dB may be attributed to the geophone acting as an accelerometer; the additional 6 dB attenuation results from the electrical response of the coil-mass moving in the magnetic field. The geophone output is nominally 90 degrees out of phase with the disturbing force but the phase response is non-linear up to about three times the natural frequency. Because of the non-linear phase response, for each component of a complex wave form there is a different phase angle between the actual driving force and the geophone output signal. Because the phase angles are not proportional to frequency, the combined pattern of the output signals is different from the combined signal pattern of the actual driving force.
As used in exploration work, an accelerometer consists of an inertial mass acting against or applying pressure to a piezo-electric crystal. The accelerometer is undamped and, because the crystal acts as a stiff spring, the natural frequency may be on the order of 600-700 Hz. The useful seismic frequency band lies well below the natural frequency of such an accelerometer. To a reasonable degree of accuracy the output of the accelerometer is 180 degrees out of phase with the driving force and, within the useful seismic frequency band, below the natural frequency of the accelerometer, the output signal suffers substantially no phase distortion. The attenuation rate vs frequency of the accelerometer output, when driven by a velocity source of constant amplitude, rises at a rate of 6 dB per octave over its useful range.
Piezo-electric hydrophones commonly used in seismic exploration at sea are sensitive to pressure changes in exactly the same way that the crystal in an accelerometer is sensitive to the pressure of an inertia mass. Accordingly, insofar as this invention is concerned, the response of a hydrophone is effectively the same as the response of an accelerometer.
To summarize the above discussion, it can be understood that the apparently obvious solution of simple integration of an accelerometer output will not yield a transfer function that will match the inherent transfer function of a selected geophone for the following reasons: First, the attenuation rate of the accelerometer, below the natural frequency of an exemplary geophone, is 6 dB per octave whereas the attenuation rate of the exemplary geophone itself is 12 dB per octave. Second, above the natural exemplary geophone frequency, the accelerometer output increases with frequency at the rate of 6 dB per octave whereas the geophone response in the same frequency band is substantially constant. Third, because of the non-linear geophone phase distortion, the pattern of signals derived from a geophone does not readily correlate with the pattern of integrated accelerometer signals at frequencies in the useful seismic band.
A more thorough theoretical treatment of seismic transducers may be found in chapter 12 of "Shock and Vibration Handbook" second edition, by C. M. Harris and C. E. Crede, McGraw Hill Book Co., New York, N.Y.
From the above discussion it will be appreciated that prior art accelerometers presently available cannot readily be substituted for geophones simply by integrating the accelerometer output signal.